In a perfect world, I'd harvest the figs (for personal use) by placing towels on the ground under the tree and waiting until they drop. Pure honey. But of course, there's the birds. I harvest a day early and do exactly the same thing you do. I see the difference in picked figs after waiting two days. If it isn't mushy (brown turkey figs) it isn't really ripe as I see it. Other varieties may not get mushy until they rot. Experiment with yours.

My figs has to fully ripen on the trees to develop the honey taste. When I buy figs from the supermarket it tastes like rubber because it did not ripen on its tree.
Birds are problem but I was able to solve it by buying few bird nets and covering all my fig producing trees. I only have four producers. The rest is very young.